Computation of Maximum Likelihood Estimates for Multiresponse Generalized Linear Mixed Models with Non-nested, Correlated Random Effects
Abstract
Estimation of generalized linear mixed models (GLMMs) with non-nested random effects structures requires approximation of high-dimensional integrals. Many existing methods are tailored to the low-dimensional integrals produced by nested designs. We explore the modifications that are required in order to adapt an EM algorithm with first-order and fully exponential Laplace approximations to a non-nested, multiple response model. The equations in the estimation routine are expressed as functions of the first four derivatives of the conditional likelihood of an arbitrary GLMM, providing a template for future applications. We apply the method to a joint Poisson-binary model for ranking sporting teams, and discuss the estimation of a correlated random effects model designed to evaluate the sensitivity of value-added models for teacher evaluation to assumptions about the missing data process. Source code in R is provided in the online supplementary material.
Keywords
Cite
@article{arxiv.1403.7676,
title = {Computation of Maximum Likelihood Estimates for Multiresponse Generalized Linear Mixed Models with Non-nested, Correlated Random Effects},
author = {Andrew T. Karl and Yan Yang and Sharon L. Lohr},
journal= {arXiv preprint arXiv:1403.7676},
year = {2014}
}
Comments
20 pages, 2 figures. Supplementary code in arXiv source package